Question

Please tell me what do i put in the blank?

Answer 1

Answer:

1. The slope of the line is -2

2. The y-intercept is 10

3. The equation in slope-intercept form is y = -2x + 10

Step-by-step explanation:

The slop-intercept form of the linear equation is y = m x + b, where

• m is the slope of the line

• b is the y-intercept (value y at x = 0)

• The rule of the slope of the line using two points on the line (x1, y1) and (x2, y2) is m = $\frac{y2-y1}{x2-x1}$

From the given table

∵ (2, 6) and (3, 4) are two points on the line

∴ x1 = 2 and y1 = 6

∴ x2 = 3 and y2 = 4

→ Substitute them in the rule of the slope above to find it

∵ m = $\frac{4-6}{3-2}$ = $\frac{-2}{1}$ = -2

∴ m = -2

∴ The slope of the line is -2 ⇒ (1)

→ Substitute it in the form of the equation above

∴ y = -2x + b

→ To find b substitute x and y in the equation by the coordinates of

    any point in the table

∵ (5, 0) is a point on the table

∴ x = 5 and y = 0

∵ 0 = -2(5) + b

∴ 0 = -10 + b

→ Add 10 to both sides

∵ 0 + 10 = -10 + 10 + b

∴ 10 = b

∴ The y-intercept is 10 ⇒ (2)

→ Substitute the value of b in the equation

∵ y = -2x + 10

∴ The equation in slope-intercept form is y = -2x + 10 ⇒ (3)